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August, 1995 A General Classification Rule for Probability Measures
Sanjeev R. Kulkarni, Ofer Zeitouni
Ann. Statist. 23(4): 1393-1407 (August, 1995). DOI: 10.1214/aos/1176324714


We consider the composite hypothesis testing problem of classifying an unknown probability distribution based on a sequence of random samples drawn according to this distribution. Specifically, if $A$ is a subset of the space of all probability measures $\mathscr{M}_1(\Sigma)$ over some compact Polish space $\Sigma$, we want to decide whether or not the unknown distribution belongs to $A$ or its complement. We propose an algorithm which leads a.s. to a correct decision for any $A$ satisfying certain structural assumptions. A refined decision procedure is also presented which, given a countable collection $A_i \subset \mathscr{M}_1(\Sigma), i = 1,2,\ldots$, each satisfying the structural assumption, will eventually determine a.s. the membership of the distribution in any finite number of the $A_i$. Applications to density estimation are discussed.


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Sanjeev R. Kulkarni. Ofer Zeitouni. "A General Classification Rule for Probability Measures." Ann. Statist. 23 (4) 1393 - 1407, August, 1995.


Published: August, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0841.62011
MathSciNet: MR1353511
Digital Object Identifier: 10.1214/aos/1176324714

Primary: 62F03
Secondary: 62G10 , 62G20

Keywords: empirical measure , Hypothesis testing , large deviations

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.23 • No. 4 • August, 1995
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